I think they're saying they run the pipeline builds using docker containers. It's how they can build easily based on any branch. Ie. what they use behind-the-scenes, not what you need to be using. Although I'm somewhat doubting myself now...

That's correct. Bitbucket Pipelines uses Docker as an execution environment for builds. However, if the goal of your build is to produce a container, whether Docker or otherwise, Bitbucket Pipelines cannot do that at this time.